IProblem 3.1.11
a) Determine the function f(t) whose Fourier transform is shown in figure P-3.l.a.
b) Determine the function f(t) whose Fourier transform is shown in figure P-3.l.b.
c) Sketch f (t) an
Integrating around the circle
signal
Fourier series coefficient
lambda(k) = 1 when k=0, equals to 0 when k!=0
=Sum of FnFn* from 0 to n
DC: component
is there a value To to make this an integer
better
0.5f1(t) + 0.5f1(t)cos2wct
+0.5f2(t)sin2wct
2 times the angular freqency
while multiply by sin or cos, it is a phase a shift
recovered f1 using lpf
at receiver
atlenuation
4piB
-2piB
2piB
-Wc
Wc
=f(t)
we want this to be as 1 as possible
if set Ac to 0, there is a problem, Ac with DC shift of f(t), it is required
for over modulation
(Am^2/Ac^2)/
(2+Am^2/Ac^2)
f^2(t) = Am^2Cos^2(Wmt)= Am^2(1/2 +1/2co
the range of f is symmetry
expression mathmatically for a modulated signal
|J1(b)| = b/2
J0(b) =1
power of sinualsdol
in cos of
From the 1st figure today, given b, Jn(b) peaks for n~= b-1
For large b,
Fall 2017
ECE 318
LAB 6
Digital Transmission
(Not marked - for interest only)
Objectives
In this experiment you will study amplitude shift keying (ASK) and binary phase shift
keying (BPSK) as digital
Chapter 5a. Introduction to Random Processes
(Section 5.2 in Textbook)
Basic concepts
Statistical averages
Wide sense stationary (WSS) processes
ECE318 - Chapter 5a
Professor W. Zhuang
1
Random pro
Laboratory: Details of experiments that supplement the lecture material can be found on LEARN.
Your timetable indicates your laboratory section and experiment dates.
Students are to work in groups o
ECE 318 - Communication Systems
Winter 2017
HW1; Signals and Systems: Solutions
Problem 1 (Haykin 2.4)
Be careful that the figure in the book uses f [Hz] as its frequency variable, whereas we
conventi
ECE 318 - Communication Systems
Winter 2017
HW2; Amplitude Modulation 1: Solutions
Problem 1 (Haykin 3.2 (a,b,c)
h
i
(a) We know i = I0 exp(
)
1
. Using the Taylor series expansion of exp(x) up to th
Figure P5.2 shows a PCM wave in which the amplitude levels of +1 volt and -1 volts are used to represent binary symbols 1 and 0 respectively. The codeword used consists of three bits. Find the sampled
Problem 4.1.1
Consider the cosine wave
g (t) = A cos(2 f0t)
Plot the spectrum of the discrete-time signal g (t) derived by sampling g (t) at the times tn = n=fs , where n = 0 1 2 and (i) fs = f0 (ii)
ECE 318 - Communication Systems
Winter 2015
Tutorial 7: Angle Modulation (Part 2)
Review
Its been three weeks since the last tutorial, so lets review some things rst.
An angle-modulated signal is gene
ECE 318 - Communication Systems
Winter 2015
Tutorial 8: Sampling
Note that the rst half of the tutorial was used to nish the problem on frequency multipliers
from Tutorial 7; the last 10-15 minutes of
ECE 318 - Communication Systems
Winter 2015
Tutorial 2: Signals and Systems
Problems
Problem 1
Suppose we have the following LTI system:
x(t)
d
dt
+
y(t)
Let x(t) be a square wave with T = 2:
1
1
rect
ECE 318 - Communication Systems
Winter 2015
Tutorial 6: Angle Modulation (Part 1)
Review
Angle modulation uses a lot of denitions, so lets review them rst.
An angle-modulated signal is generally given
ECE 318 - Communication Systems
Winter 2015
Tutorial 5: Amplitude Modulation (SSB and VSB)
Problems
Problem 1 (Haykin 3.19)
Shown below is a Weaver modulator, which allows us to generate single-sideba
ECE 318 - Communication Systems
Winter 2015
Tutorial 3: Amplitude Modulation (DSB-LC)
Problems
Problem 1
Consider the following DSB-LC modulator. Let the bandwidth of f (t) be B [rad/s]. Assume
the fo
ECE 318 - Communication Systems
Winter 2015
Tutorial 4: Amplitude Modulation (DSB-SC and QCM)
Problems
Problem 1
Two signals f1 (t) and f2 (t) with corresponding spectra shown below are to be transmit
ECE 318 - Communication Systems
Winter 2015
Tutorial 1: Review of Signals and Systems
Fourier transform
In this course, we will be using the following convention for the Fourier transform and its
inve
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ECE318 Mathematical Background
Preamble
The following are mathematical concepts and questions that have appeared in previous offerings of the
ECE 318 course. Solving these questions can help you to se
ECE318 Mathematical Background
Preamble
The following are mathematical concepts and questions that have appeared in previous offerings of the
ECE 318 course. Solving these questions can help you to se
ECE 318 - Communication Systems
Winter 2017
HW2; Amplitude Modulation 1: Problems
Problem 1 (Haykin 3.2 (a,b,c) In part b, instead of determining the spectrum, only determine the frequencies that are
ECE318: Communication Systems, Fall 2011
Department of Electrical and Computer Engineering, University of Waterloo
Instructor: Prof. Zhou Wang
Homework 3
Problem 1
Problem 2
Problem 3
Repeat Problem 2